CARPENTRY. 



Theory of the openings which are to be seen among the leaves; 

 tr J- they afford much room for observation, .md will be 

 ' """ found to give good notions of the- effect of the trans- 

 verse strain ; the parcel may he bent so much, that 

 every leaf will separate to the very last, winch there- 

 fore is the only one that resists the folding by its 

 cohesion. The open part of the rest shows us the 

 form of the splinter IRS, Fig. !5. which would fly 

 off, were not the matter so coherent. It is some- 

 what triangular, and the direction of its sides appears 

 to be much the name with KD, and its correspondent 

 on the opposite side. Slacken the parcel on one side, 

 and pinching again, observe the slide which has taken 

 pk'.-i 1 among the leaves. Thus the cohesion of the 

 ligneous beds has an important effect in the transverse 

 strength of beams. And, of balks cut out of the 

 same tree in different ways, that in which the layers 

 are placed on edge, will always bear much more than 

 that in which they lie on their sides. This cohesion 

 is not only useful in preventing slipping, but also in 

 preventing the fibres on the concave side from part- 

 ing too easily from the rest. This consideration is 

 ot importance, especially in the building up of gir- 

 ders, and the formation of masts. It shows that we 

 must not be too hasty in saying, that fir should al- 

 ways be chosen for the sides made hollow by the 

 strain, in preference to oak, merely because it is 

 stronger as a pillar, though oak be tougher as a tie. 

 There are other circumstances to be thought of. 

 The fibres of fir have little lateral cohesion ; and un- 

 less we can secure them, and contrive to bring them 

 all into action, we may be led into serious mistakes. 

 But let us now examine the mathematical conse- 

 quences which this last supposition involves. Let 



: 'g. * ARSB, Fig. 4-., be the vertical section of a beam 

 so constituted, that when the beam is loaded at one 

 end with the weight W, the fibres in CR are in a 

 state of compression ; while tfease in CA are in a state 

 of extension, that in the instant of fracture any par- 

 ticle in CA, as E, adheres by the force Ee, and one 

 in CR, as F, resists or repels with the force F^ 

 The force of each particle being expressed in this 

 way, some line a D r, limits the whole of these or- 

 dinates, and the area a D A, expresses the total 

 force of adhesion, while DRr expresses the force of 

 repulsion. Should the force of each particle be pro- 

 portional to the extension or compression, which is 

 highly probable, at least for the safer strains, then 

 D ana D r will be straight lines ; and if the resist- 

 ance to compression be exactly equal to the resistance 

 to a similar extension, a D r will be one straight line. 

 But this is not to be expected ; for in most bodies 

 which are tolerably firm, the resistance to compression 

 is likely to be the most considerable ; and therefore 

 the ordinates E e are likely to be smaller than F/. 

 But since the weight W is understood to act perpen- 

 dicularly to the length of the beam, the adhesion and 

 repulsion in the section of fracture must be equal, and 

 therefore the area of AD a equal to the area DRr. 

 Now we have said, that in firm bodies, for the most 

 part, the ordinates E e are smaller than F/J the per- 

 pendicular AD must therefore be longer than DR, 

 and the neutral point D nearer the lower side of the 

 beam. 



In soft and compressible bodies, RD may equal 



or even exceed AD. The experiments of Duhamcl Thtorjr 01 



bhow this to be remarkably the case in willow, and 



He took 2t pieces of young willow, 



the same bise, and formed them into bar* 



of :' feel long, 1 \ inch square, taking care to have the 



heart of the tree in the cei.tre ; supporting these by 



props ^ths of an inch from each end, he broke them 



by weights hung on at the middle. 



The mean weight borne by MX entire bar was 

 524 Ibs. 



He next cut two of the bars one-third through 

 with the saw, and filled up the draft with a wedge of 

 dry oak. The mean of these was 551 Ibs. 



He cut two ethers one half through, and wedged 

 up the cut as before ; and although one of them broke 

 short on account of a concealed knot on the lower 

 side, yet the mean of weight borne by these was 

 512 Ibs. 



He cut another set of six bars, three quarter* 

 through in the same way, and the mean weight borne 

 was 530J Ibs. 



It is worthy of remark, that one of these last, 

 when loaded with 4-35 Ibs. was unloaded, and a thicker 

 wedge put in place of the first slip of oak, it then 

 broke only with 576' Ibs. Had it been successively 

 supplied with thicker wedges, it might possibly have 

 carried a great deal more. 



From these experiments, it is evident that more 

 than two-thirds of the thickness, or perhaps three- 

 fourths of it, does not contribute by its tension to 

 the strength of the original bar. The compressibi- 

 lity of this kind of timber, appears much greater than 

 its dilatability, and some other experiments of Du- 

 hamel seem to confirm this. 



He has also given us some experiments on Baltic 

 fir. The battens he employed were three feet long, 

 fifteen lines thick, and seven broad. 



Two such bars, when entire, bore 144 Ibs. 9oz. 

 at a medium ; three bars sawn one-third through in 

 four places, and the cuts fitted with slips of hard 

 wood, bore 132 Ibs. 2oz. 



Two others, cut half way through in four places, 

 bore Hb'lbs. 7oz. 



Two others, cut two- thirds through in four places, 

 bore 136' Ibs. 15 oz. 



One bar had a cut made on one side of a foot long, 

 and half an inch deep, the space filled with a piece 

 of oak, it bore 509 Ibs. 



Another, when the cut was only one-fourth of an 

 inch deep, bore 551 Ibs. 



An entire bar, of equal dimensions, bore 576 Ibs. 

 nearly. 



Observe that the oak is more compressible than 

 the fir. 



The point D being the centre of fracture, the 

 centre of effort of the attractive forces will be found 

 as in the last hypothesis. Let this be E, if the beam 

 AS be a rectangular prism, the distance DE is one- 

 third of DA. In like manner, the centre of the re- 

 pulsive forces F will be similarly situated with respect 

 to the line AR. The distance between these two 

 points will be the shorter arm of the lever, by the 

 energy of which, the force of attraction resists the 

 effort of the weight W, while the centre of repul- 

 sions serves as the fulcrum j or if we choose to con- 



